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Approximation error

About: Approximation error is a(n) research topic. Over the lifetime, 9390 publication(s) have been published within this topic receiving 191605 citation(s).

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Papers
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Open accessJournal ArticleDOI: 10.1214/AOMS/1177729586
Herbert Robbins1, Sutton Monro1Institutions (1)
Abstract: Let M(x) denote the expected value at level x of the response to a certain experiment. M(x) is assumed to be a monotone function of x but is unknown to the experimenter, and it is desired to find the solution x = θ of the equation M(x) = α, where a is a given constant. We give a method for making successive experiments at levels x1, x2, ··· in such a way that xn will tend to θ in probability.

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7,621 Citations


Journal ArticleDOI: 10.1109/18.256500
Andrew R. Barron1Institutions (1)
Abstract: Approximation properties of a class of artificial neural networks are established. It is shown that feedforward networks with one layer of sigmoidal nonlinearities achieve integrated squared error of order O(1/n), where n is the number of nodes. The approximated function is assumed to have a bound on the first moment of the magnitude distribution of the Fourier transform. The nonlinear parameters associated with the sigmoidal nodes, as well as the parameters of linear combination, are adjusted in the approximation. In contrast, it is shown that for series expansions with n terms, in which only the parameters of linear combination are adjusted, the integrated squared approximation error cannot be made smaller than order 1/n/sup 2/d/ uniformly for functions satisfying the same smoothness assumption, where d is the dimension of the input to the function. For the class of functions examined, the approximation rate and the parsimony of the parameterization of the networks are shown to be advantageous in high-dimensional settings. >

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Topics: Approximation error (59%), Linear approximation (58%), Function approximation (58%) ...read more

2,519 Citations


Open accessJournal ArticleDOI: 10.1007/S11263-010-0390-2
Simon Baker1, Daniel Scharstein2, John P. Lewis3, Stefan Roth4  +2 moreInstitutions (5)
Abstract: The quantitative evaluation of optical flow algorithms by Barron et al. (1994) led to significant advances in performance. The challenges for optical flow algorithms today go beyond the datasets and evaluation methods proposed in that paper. Instead, they center on problems associated with complex natural scenes, including nonrigid motion, real sensor noise, and motion discontinuities. We propose a new set of benchmarks and evaluation methods for the next generation of optical flow algorithms. To that end, we contribute four types of data to test different aspects of optical flow algorithms: (1) sequences with nonrigid motion where the ground-truth flow is determined by tracking hidden fluorescent texture, (2) realistic synthetic sequences, (3) high frame-rate video used to study interpolation error, and (4) modified stereo sequences of static scenes. In addition to the average angular error used by Barron et al., we compute the absolute flow endpoint error, measures for frame interpolation error, improved statistics, and results at motion discontinuities and in textureless regions. In October 2007, we published the performance of several well-known methods on a preliminary version of our data to establish the current state of the art. We also made the data freely available on the web at http://vision.middlebury.edu/flow/ . Subsequently a number of researchers have uploaded their results to our website and published papers using the data. A significant improvement in performance has already been achieved. In this paper we analyze the results obtained to date and draw a large number of conclusions from them.

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Topics: Optical flow (61%), Motion interpolation (56%), Approximation error (51%) ...read more

2,371 Citations


Open accessJournal ArticleDOI: 10.1109/9.119632
James C. Spall1Institutions (1)
Abstract: The problem of finding a root of the multivariate gradient equation that arises in function minimization is considered. When only noisy measurements of the function are available, a stochastic approximation (SA) algorithm for the general Kiefer-Wolfowitz type is appropriate for estimating the root. The paper presents an SA algorithm that is based on a simultaneous perturbation gradient approximation instead of the standard finite-difference approximation of Keifer-Wolfowitz type procedures. Theory and numerical experience indicate that the algorithm can be significantly more efficient than the standard algorithms in large-dimensional problems. >

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1,912 Citations


Open accessJournal ArticleDOI: 10.1111/1467-8659.00236
Abstract: This paper presents a new tool, Metro, designed to compensate for a deficiency in many simplification methods proposed in literature. Metro allows one to compare the difference between a pair of surfaces (e.g. a triangulated mesh and its simplified representation) by adopting a surface sampling approach. It has been designed as a highly general tool, and it does no assuption on the particular approach used to build the simplified representation. It returns both numerical results (meshes areas and volumes, maximum and mean error, etc.) and visual results, by coloring the input surface according to the approximation error. EMAIL:: r.scopigno@cnuce.cnr.it

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  • Figure 1: A mesh simpli cation example: the original mesh (7,960 triangles) is on the left, a simpli ed one (179 triangles) is on the right.
    Figure 1: A mesh simpli cation example: the original mesh (7,960 triangles) is on the left, a simpli ed one (179 triangles) is on the right.
  • Figure 2: Signed distance evaluation; distance is positive in p1 and negative in p2 (S1 is the sampled curve).
    Figure 2: Signed distance evaluation; distance is positive in p1 and negative in p2 (S1 is the sampled curve).
  • Table 1: Number of sampling points, sampling step size, time and number of faces tested per sample on three di erent meshes.
    Table 1: Number of sampling points, sampling step size, time and number of faces tested per sample on three di erent meshes.
  • Figure 6: Di erent color mapping modality: per-vertex mapping on the left, and error-texture mapping on the right.
    Figure 6: Di erent color mapping modality: per-vertex mapping on the left, and error-texture mapping on the right.
  • Figure 7: Color may be mapped considering the sign of the error (i.e. the sign of the evaluated distance, de ned only for orientable meshes).
    Figure 7: Color may be mapped considering the sign of the error (i.e. the sign of the evaluated distance, de ned only for orientable meshes).
Topics: Approximation error (56%), Progressive meshes (52%), Polygon mesh (50%)

1,480 Citations


Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202213
2021508
2020499
2019465
2018448
2017412

Top Attributes

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Topic's top 5 most impactful authors

Jari P. Kaipio

34 papers, 1.1K citations

Yuichi Kida

14 papers, 39 citations

Takuro Kida

14 papers, 32 citations

Tanja Tarvainen

13 papers, 396 citations

Michael Unser

12 papers, 395 citations

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